A short treatise on the equivariant degree theory and its applications

The aim of this survey is to give a profound introduction to equivariant degree theory, avoiding as far as possible technical details and highly theoretical background. We describe the equivariant degree and its relation to the Brouwer degree for several classes of symmetry groups, including also the equivariant gradient degree, and particularly emphasizing the algebraic, analytical, and topological tools for its effective calculation, the latter being illustrated by six concrete examples. The paper concludes with a brief sketch of the construction and interpretation of the equivariant degree.